Default priors for Bayesian (brms) delay-discounting models

Returns the default prior table used by fit_dd_brms(), so the defaults can be inspected, modified row-wise, and passed back via the fitter's prior argument. The logk location is the principled fix for k's delay-unit dependence: with autoscale = TRUE (the default whenever data is supplied) it centers k * median(delay) = 1 – the delay at which the Mazur curve crosses 0.5 – via normal(-log(median(x)), 2.5); the static fallback is normal(-4.5, 2.5). The anchors used are attached as attr(, "autoscale_info"); numeric values are formatted with format(x, digits = 6, scientific = FALSE).

Usage

default_dd_priors(
  equation = c("mazur", "exponential", "green-myerson", "rachlin"),
  family = c("beta", "gaussian"),
  data = NULL,
  y_var = "y",
  x_var = "x",
  factors = NULL,
  factor_interaction = FALSE,
  continuous_covariates = NULL,
  autoscale = !is.null(data),
  random_effects = k ~ 1,
  covariance_structure = c("pdSymm", "pdDiag")
)

Arguments

equation

Discounting equation (TMB-tier vocabulary).

family

"beta" or "gaussian".

data

Optional data frame used for autoscaling.

y_var, x_var

Column names in data (canonical defaults).

factors, factor_interaction, continuous_covariates

Fixed-effect design on logk, as passed to the fitter. When the design has non-intercept coefficients (derived through build_fixed_rhs(), so single-level dropped factors do not count), a fold-change normal(0, 1) class-level coefficient prior is added; with an intercept-only design it is omitted (it would be unused, and brms warns).

autoscale

Logical; defaults to TRUE when data is supplied.

random_effects

k ~ 1 (default) or k + phi ~ 1. The latter re-keys the beta precision: phi becomes a predicted distributional parameter, so the scalar gamma(2, 0.1) is replaced by a log-scale intercept prior, a half-t precision-RE SD, and (for "pdSymm") an LKJ correlation prior.

covariance_structure

(log k, log phi) covariance for k + phi ~ 1: "pdSymm" (default, correlated) or "pdDiag" (independent).

Value

A brmsprior data frame, with attr(, "autoscale_info") when autoscaling was used.

Details

Other defaults: logs ~ normal(0, 0.5) (two-parameter equations; s is near 1 a priori), sd(logk) ~ student_t(3, 0, 1), phi ~ gamma(2, 0.1) (Beta precision; mean 20, far from brms's near-improper gamma(0.01, 0.01)), and sigma ~ student_t(3, 0, 0.25) for the Gaussian family (y is a proportion in the unit interval, so sd(y) <= 0.5).